No and no.

You might be interested in Travis Norsen's "Foundations of Quantum Mechanics," which would give you an Objectivist physicist's perspective on quantum theory. If you're really serious about studying Oism, you could join Dr. Binswanger's (paid) online discussion forum at hbletter.com.

On the analytic/synthetic dichotomy, start with Peikoff's essay on that subject in "Introduction to Objectivist Epistemology." There are also resources on the Ayn Rand Institute's website, and on their YouTube channels (their UK channel publishes tons of content).

Peikoff's "Objectivist Philosophy of Ayn Rand" was approved by Rand and is essential for understanding Objectivism. I would also recommend reading Blackwell publishing's "A Companion to Ayn Rand." As to your specific concerns...

. . . as far as *you* know. In fact, these kinds of concerns have been addressed by Objectivist philosophers in print, recorded lectures, podcasts, etc. The resources are there if you are genuinely interested in investigating.

Incorrect. Read her “Introduction to Objectivist Epistemology,” then read “How We Know” by Harry Binswanger.

Rand was focused on presenting her own philosophy rather than in providing formal critiques of those she opposed. Other Objectivists have discussed her objections in detail (in some cases with her input and approval).

Then I respectfully suggest giving Ayn Rand an honest look. Check out her “Introduction to Objectivist Epistemology.” And thank you for your work, especially “Philosophy Bites.”